A Bayesian nonparametric approach to discriminant analysis

We introduce a Bayesian nonparametric framework to improve classical discriminant analysis, particularly in scenarios with limited sample sizes. The proposed method provides a flexible approach that encompasses both linear and quadratic discriminant analysis as special cases. Its key innovation lies in allowing information sharing across classes to improve the estimation of the class-specific covariance matrices. This is accomplished through a scale-only nonparametric mixture model defined on the space of positive definite matrices. A conjugate nonparametric prior ensures remarkable ease of implementation and tractability, allowing the analytical derivation of posterior distributions for several quantities of interest and facilitating the study of their large-sample properties. Applications to both simulated and real datasets demonstrate the adaptability and effectiveness of the proposed methodology.